i own a casio excilim z3 and im very pleased with it, the colors of the photos are great and better than many other much more expensive camaras. the overall quality is good although it blurs slightly in the edges, which is a problem some camaras have. another thing that i dont like about it is that im not able to specify the actual time and aperture of each photo, i can set it to long exposure etc, but i cant select the values manually, which would be good (but i belive the newer exilim models z40 and z50, can)
some specs u need to take attention:
_resolution: mine is 4 megapixels which i think is enough, the maximum size is 2300*something
_the size of the screen is very important, because u cant see clearly if the photo is blured and if everythings alright when it is small
_zoom, what matters is the optical zoom, forget the digital, mines has 3x optical zoom
_dimensions, i like to be able to carry the camara all the time without having to carry an extra case!
_aspherical lens. spherical lens distort the image, if your camara has aspherical lens, thats great
_focus range, macro. macro pictures allways looks cool

so its good to have a macro that can focus from a very small distance
_aperture, its good to have a wide range of apertures, remember the number is inverse of the aperture, so F2.1 is wide opened and F5 is very small (im sorry i dont know the terminology in english)
_shutter speed, averture is closely connected to shutter speed
if u are in a dark place you need to choose a wide averture so that it receives more light without having to stay opened for a long time (shutter speed)
if your catching a motion scene you want it to appear still (or not, but lets pretend u do

) so u need to take your picture very fast so that the object doesnt move a lot while the shutter is opened, in this case u also want the shutter to be wide opened, otherwise the picture gets too dark
theres a problem with wide opened shutters, its harder to focus, u can understand it if u think about the rays of light that pass through the shutter. if it is too opened only the object that you were trying to focus will appear crisp, everything else will be blured.. this is cool for taking portraits, usually u dont want to focus the background, and when it is blured it helps to had a more dramatic mood.
White balance, this is one of the most important thing in a photograph, belive me, and lots of people dont really know what it is. everything can stay automatic but Never Ever use automatic white balance, because our eye adapts to the color of the light, but the camara doesnt, so it tryes to compensate the colors but usually it comes out too blue or too orange.
usually camaras have some templates for white balance, direct sun, shadow, etc. but u should manually ajust whenever it is possible, they recomend to use a white paper as reference (be carefull, some papers are slightly yellow which would cause the picture to appear blue!) so u need to place something white in front of the camara to calibrate the white balance... but if u dont have anything white nearby u can use grey or black

it works well too.
now that u know something about photography u can start to practice.. that when ull really begin to learn usefull things

good luck, and post pictures!